The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this study. Based on Lyapunov–Krasovskii theory the proposed methods formulated as linear matrix inequality problems are able to check the stability interval when the time-varying delay d(t) belongs to an interval [τ₁, τ₂]. The Lyapunov–Krasovskii functional (LKF) selected in the present paper is simpler than some ones considered in the literature. However, the criteria obtained, based on this simple LKF, outperformed the similar existing ones in all numerical tests accomplished in this paper.

Notation: Through out this paper the superscript T stands for transpose. 0 refers to a null matrix with appropriate dimensions. For a real symmetric matrix M, the notation M > 0 ( < 0) means that M is the positive (negative) definite. The symmetric term in a matrix is denoted by *.

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Further improvement in stability criteria for linear systems with interval time-varying delay

References

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